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medians of triangle are sidelengths of a right triangle

Source: Sharygin Geometry Olympiad 2016 Final Round problem 1 grade 8

July 22, 2018
geometryMediansright trianglealtitude

Problem Statement

An altitude AHAH of triangle ABCABC bisects a median BMBM. Prove that the medians of triangle ABMABM are sidelengths of a right-angled triangle.
by Yu.Blinkov